Systems that include electronic elements (e.g., resistors, capacitors, inductors, voltage sources, etc.) and mechanical elements (e.g., springs, levers, oscillating arms, etc.) can be difficult to analyze. An exemplary method for analyzing such a system includes the derivation of transfer functions of the system, wherein the transfer functions can be employed in connection with finding electronic or mechanical resonant frequencies of the system, as well as in connection with designing, optimizing, and/or validating controllers used in the system.
Deriving transfer functions of a system that includes electronic and/or mechanical elements, however, is nontrivial. An exemplary approach for deriving transfer functions of a system is to estimate an input to the system (e.g., selecting a first mathematical function that represents a controlled source of energy) and also estimating the output of the system (e.g., selecting a second mathematical function that is believed to represent the output of the system). Based upon the estimated system input and system output, the transfer functions of the system can be derived. Estimating the system input and system output, however, is often associated with inaccuracies. For instance, a conventional approach for estimating input and output of a system involves simulation of the system in the time domain, wherein the input to the system is modified during simulation and corresponding output of the system is recorded. The simulated system input and output are then subjected to transformations to generate frequency domain signals. Transfer functions (in the frequency domain) of the simulated system are then computed based upon the frequency domain signals corresponding to the simulated input and simulated output.
This conventional approach, however, suffers from various deficiencies. First, simulating operation of the system is a nontrivial task, and typically requires a user that is performing such simulating to have a relatively large amount of knowledge about the system to ensure that the system remains stable during simulation. Additionally, a relatively large amount of simulation needs to be performed to compute transfer functions accurately. The process of simulation and conversion from the time domain to the frequency domain is computationally expensive, and can take several days for relatively complex systems using conventional computing devices. Additionally, if the system is modified (e.g., if an element is added, removed, or modified), the entire process must be repeated.